Magnetic resonance imaging (MRI) is a common and well known technique for imaging the internal structure of objects and for medical diagnosis. MRI requires that the object to be imaged be placed in a uniform (typically to within 40 ppm) and strong (typically in the range of 0.5 to 1.5 Tesla) magnetic field. Generating such magnetic fields is difficult and expensive.
Prepolarized MRI (PMRI) is a new technique which uses a strong, nonuniform pulsed magnetic field in combination with a weaker, uniform magnetic field to perform imaging. PMRI is also referred to as switched-field MRI in the literature. Reference can be made to U.S. Pat. No. 5,629,624 to Carlson et al. and U.S. Pat. No. 5,057,776 to Macovski concerning PMRI.
Since the magnetic field in a PMRI device must be pulsed, researchers have experienced severe difficulties in obtaining pulse-to-pulse consistency of the magnetic field. These difficulties can be caused by ferromagnetic pole pieces which experience magnetic hysteresis. The hysteresis changes the magnetic field distribution in unpredictable ways. Therefore, it is believed that ferromagnetic pole pieces are incompatible with PMRI without significant control over hysteresis.
Another result of the pulsed magnetic field is that it renders a large PMRI device very difficult to build. The magnetic energy stored in the magnet must be removed and restored with every pulse. This practically limits the amount of energy which can be stored in the pulsed magnet and thus the size of the PMRI device. Therefore, future PMRI devices will likely be small dedicated imagers, dedicated to imaging small body parts such as hands, feet, knees, heads, breasts, neck and the like.
Imaging small body parts places limitations on magnet geometry. Most body parts are not cylindrical and therefore do not efficiently occupy the volume inside a traditional cylindrical magnet assembly. A cylindrical magnet assembly is a collection of coils arranged on the surface of a cylinder. Most body parts are asymmetric and therefore an asymmetric magnet designed with a particular body part in mind would likely provide a more uniform field with less power consumption compared to a cylindrical magnet for imaging the same body part. The operation of dedicated MRI scanners could be substantially improved by effective asymmetric magnet designs.
Another concern with PMRI devices is that it is best for the electromagnet which provides the pulsed field (the polarizing magnet) to be a separate magnet from the magnet which provides the uniform field (the read-out magnet). Therefore, to build a PMRI device, the read-out magnet and the polarizing magnet must fit together such that the pulsed field from the polarizing magnet and the uniform field from the read-out magnet overlap. The problem of designing mechanically compatible read-out and polarizing magnets is greatly simplified if the read-out magnet is asymmetric.
However, it is very difficult with present magnet design techniques to design magnets of arbitrary geometry which produce uniform magnetic fields or any specific predetermined magnetic field. It is particularly difficult to design asymmetric magnets such that they consume a minimum of electrical power for a given desired field. Some magnet designs unnecessarily utilize `negative currents` to provide a uniform field, but at the expense of greatly increased power consumption. It would be an advance in the art of MRI to be able to design asymmetric magnets in accordance with arbitrary geometrical constraints which consume a minimum of power. Also, it would be an advance in the art to provide a magnet design technique which designs magnets using negative currents only when absolutely necessary.
Asymmetric magnets are not commonly used in MRI or in other applications which require strong, uniform magnetic fields. The term `asymmetric` herein refers to asymmetry across a plane perpendicular to the axis of rotational symmetry. FIG. 1A shows a cross sectional view of an symmetric magnet and FIG. 1B shows an example of a asymmetric magnet. Asymmetric magnets are not used because they are difficult to design, and particularly difficult to design such that they consume minimal power. This is unfortunate because asymmetric magnet designs can increase access to the magnetic field. Particularly, asymmetric magnet designs could improve the operation of and lower the cost of dedicated MRI scanners for scanning specific body parts.
Asymmetric magnets which provide uniform fields could also be used in any application which requires inexpensive, high performance magnets of arbitrary geometry.
More generally, the art of magnet design could benefit from a technique for designing magnets which can always find the lowest power coil layout for a desired magnetic field. Often, the coil layout which consumes the least power is also the cheapest to build. It would be an additional benefit if a magnet design technique could design magnets to conform to arbitrary geometrical constraints.
U.S. Pat. No. 4,721,914 to Fukushima et al. discloses an asymmetric magnet design which uses two coils having different radii. Fukushima's apparatus is limited to asymmetric magnets with two coils and cannot provide magnets which are compatible with arbitrary geometrical constraints. Also, Fukushima's apparatus produces an impractically inhomogeneous magnetic field for use with MRI devices.
U.S. Pat. No. 5,250,901 to Kaufman et al. discloses an asymmetric magnet having a single coil. The apparatus of Kaufman is limited in that Kaufman does not disclose asymmetric designs having more than one coil. Also, Kaufman relies upon ferromagnetic yokes. Ferromagnetic yokes are not compatible with some magnet applications such as PMRI which requires pulsed fields.
U.S. Pat. No. 5,659,281 to Pissanetzky et al. discloses a method for designing electromagnets and magnets which can be designed by the method. Pissanetzky's method often relies heavily on negative currents to achieve field homogeneity and therefore in many cases resistive electromagnet designs arrived at by Pissanetzky's method will not consume the least power possible for a desired field and desired magnet geometry. Analogously, superconducting magnet designs arrived at by Pissanetzky's method will not utilize the shortest length of superconducting wire possible. Pissanetzky's magnets are also characterized in that some of the magnet coils will have different current densities. Electromagnet coils designed for the same current density have the advantage that they can be connected in series and simply manufactured using wire of uniform size throughout.
Homogenous magnet designs with a small (typically less than 12) number of coils require the selection of the z location, radii and currents for each coil. The field profile is a non-linear function of the coils' z location and radii, whereas it is a linear function of the current. Hence, most classical magnet design techniques developed to date use non-linear optimization algorithms, which tend to be slow and are not guaranteed to converge to a reasonable magnet design. It would be an advance in the art of magnet design to find a method that did not require nonlinear optimization.
Hoult (Journal of Magnetic Resonance, 1994, vol 108, no 9, 1994) proposed a method to implements a concept using a pseudoinverse matrix to calculate coil currents in each of a number of virtual coils. The technique minimizes the magnet power (a virtue of the pseudoinverse algorithm) subject to exactly enforcing the homogeneity constraint. However, Hoult's technique does not minimize the number of coils, so a magnet built according to Hoult requires an impractical number of coils. In fact, a magnet built according to Hoult will have the same number of coils as the number of virtual coils used in the calculation.
Kitamura (1994, IEEE Transactions on Magnetics, Vol 30, no.4, page 2352) discloses a technique for minimizing the total volume of superconducting wire subject to constraints on the size of the spherical harmonic coefficients (a measure of field inhomogeneity). Kitimura's method can only design magnets which produce a spherical predetermined field. The initial phase of Kitamura's algorithm develops an initial current distribution on a cylinder that serves as a starting point for further nonlinear calculations with a superconducting coil and ferrous yoke.